How does one convert two-line elements to some other
format? Actually, this is one of the most common questions I get asked.
Usually, the user has data in some other format that they want to use in a
program that uses two-line element sets or they have two-line element set data
that they want to use in their favorite satellite-tracking program. The simple
answer is: Just don't do it! Here's why.

The common misconception is that the two-line element sets are simply a
format for standard data. After all, if both the two-line element set format and
Format X have an eccentricity term, it should be a simple matter of substituting
the value. Other terms could simply be interchanged by using a straightforward
mathematical transformation (such as the relationship between mean motion and
semi-major axis). Isn't there a program to automatically handle this conversion?
Unfortunately, it's not quite that simple.

The elements in the two-line element sets are mean elements calculated to fit
a set of observations using a specific model—the SGP4/SDP4 orbital model.
Just as you shouldn't expect the arithmetic and geometric means of a set of data
to have the same value, you shouldn't expect mean elements from different
element sets—calculated using different orbital models—to have the
same value. The short answer is that you cannot simply reformat the data unless
you are willing to accept predictions with unpredictable errors. The long answer
is that I will discuss a method for transforming element sets—which
involves a much more complicated process—in a future column.

What is the accuracy of predictions using the two-line
element sets? Accuracy of the two-line element sets is dependent upon a
number of factors. These range from the particular sensors used and amount of
data collected to the type of orbit and condition of the space environment.
Unfortunately, since these factors vary for each element set, so does the
accuracy. While NORAD has experimented with methods to incorporate prediction
quality into the element sets, none of these methods has yet proved
successful.

It is possible, however, to assess the consistency of the element set
data, rather than their accuracy. That is, how well one element set's
predictions agree with those of its successor or predecessor element set. By
comparing the magnitude of the vector difference of the predictions from two
successive element sets at the epoch of the newer element set (when it should be
most accurate), it is possible to gauge the consistency between those element
sets. Taken in aggregate for a particular satellite over time, it is possible to
gauge the general accuracy of the data (assuming that the element set production
process is statistically unbiased) and get a sense for how long an element set
is valid.

While NORAD maintains specific target tolerances for the overall level of
accuracy as a system performance metric, it can be expected that accuracy will
vary depending upon the type of orbit and satellite involved. For this reason,
it is probably best to independently assess the accuracy of each specific
satellite for which accuracy is a consideration. For more information on this
topic, see my column titled "Real-World
Benchmarking" in Satellite Times Volume 3 Number 2.

How often are element sets generated? New element
sets are generated by NORAD on an as-needed basis rather than according to an
established timetable. How often these updates occur depends upon a number of
factors such as the orbit type or maneuvering capability of the satellite. For
example, a satellite in low-earth orbit—such as the US space
shuttle—would have its element sets updated several times a day because of
the somewhat unpredictable results of atmospheric drag as it varies its attitude
and the maneuvering being performed. A satellite in a low-drag orbit which
doesn't maneuver—such as LAGEOS II—might only need updates once
or twice a week. Objects such as rocket bodies, defunct payloads, or other space
debris, won't be updated as frequently, either—unless there is a
prediction of a close approach with an operational payload. Special-interest
objects—such as a large object reentering the earth's
atmosphere—normally get special treatment.

What is the reference frame of the resulting
coordinates? This question is a bit more technical than most we have
covered. To be precise, the reference frame of the Earth-centered inertial (ECI)
coordinates produced by the SGP4/SDP4 orbital model is true equator, mean
equinox (TEME) of epoch.

In layman's terms, this simply means that the cartesian coordinates produced
by the SGP4/SDP4 model have their z axis aligned with the true
(instantaneous) North pole and the x axis aligned with the mean direction
of the vernal equinox (accounting for precession but not nutation). This
actually makes sense since the observations are collected from a network of
sensors fixed to the earth's surface (and referenced to the true equator) but
the position of the earth in inertial space (relative to the vernal equinox)
must be estimated. For more details on this coordinate system, see my article on
"Orbital Coordinate Systems, Part I" in
Satellite Times Volume 2 Number 1.

Are there two-line element sets for the moon and/or
sun? The short answer to this question is no. Assumptions made in the
SGP4/SDP4 orbital model—made to reduce the computational burden of
tracking thousands of earth satellites—are completely invalid when applied
to other celestial bodies. Details on why this is so were covered in the
January/February 1997 issue of this column titled—naturally
enough—"Tracking the Sun and the Moon." If
you want to track the sun, moon, planets, or the latest comet, you're going to
need to use an orbital model specifically designed to track these objects.

How do new satellite elements get added to the CelesTrak
WWW? Normally, all new objects are added to the master list as soon as
the object is catalogued by NORAD. After 30 days have elapsed, elements are only
maintained if someone requests that they be—otherwise, they are removed.
At present, the master list contains a broad range of satellite element sets
used by a large number of people around the world. It contains elements for
various communications, navigation, weather, and other scientific satellites.
Over the years, it has grown to include 300 satellite element sets.

The master list was originally intended as a single source of distribution
back when this was originally done via the Celestial BBS and (later) the
Usenet newsgroups. However, many users are interested in only a particular
category of satellites for their applications, such as amateur radio satellites,
and don't want a large list. As such, the CelesTrak WWW breaks out the
satellite element sets into separate categorical lists to make it easier to find
the elements of interest to you. Check out the Current Data section to see what lists are
currently available.

In the future, the master list will probably be replaced with a list which
contains only new objects catalogued within the past 30 days. All other elements
will be contained within the individual categorical lists. Eventually, I hope to
be able to provide users an option of defining their own list of elements to
provide the ultimate in customization.

How does one find source code for the SGP4/SDP4 orbital
models? The primary source for the SGP4/SDP4 orbital models is found in
Spacetrack Report Number 3: Models for Propagation of NORAD Element Sets.
It contains the equations for most of the model along with the associated
FORTRAN source code. This
document is available on the
CelesTrak WWW in Adobe Acrobat Portable Document Format (PDF). The
FORTRAN source code can be copied directly from this document and pasted into
any text editor. There is also a
LATEX
version online.

If you need source code in some language other than FORTRAN, you can also
find a Pascal version of the complete SGP4/SDP4 orbital model on the CelesTrak
WWW in my SGP4 Pascal
Library. It contains not only the NORAD orbital model, but routines for
doing various coordinate transformations and calculating the position of the
sun. These routines were used to develop my
TrakStar
program—a simple program intended to show how easy it is to use the
library but often used as a standalone analysis tool. While I still plan to
produce a C version of this code, I have not had time to do this yet and I know
of no publicly-available C version which contains both the SGP4 and SDP4
orbital models.

How does one obtain historical element sets? As of
mid-January 1998, there is now an online
form on the CelesTrak WWW to request historical two-line element
sets. Current archives run from January 1980 through the present and contain
over ten million two-line element sets. Those historical element sets which are
requested frequently are kept online in the
Historical Archives section. However, it
is impossible to keep all of the current archives—over 1.5 gigabytes of
data—online. If you have a need for historical data which cannot be found
online, please use this form (found at the bottom of the main Historical
Archives page) to request the data you need.

Where does one find a list of satellite
frequencies? The best source of information on satellite downlink
frequencies that I've seen can be found on Launchspace.com in their
Reference section. It contains a list of over 600 downlink frequencies in
the range of 3 MHz to 32 GHz covering everything from satellites to NASA support
aircraft [Launchspace no longer carries this list of satellite frequencies.
If I find another source, I'll include it here.].

Correction: In my last column ("Frequently Asked Questions: Two-Line Element Set
Format"Satellite Times Volume 4 Number 3), I suggested that the
format for fields 1.10 and 1.11 owed its heritage to the FORTRAN programming
language. Instead, as one of our readers pointed out, it originated with the
Philco 2000/Model 212 and the TAC assembly language used on the original 496L
system. The FORTRAN language just happens to follow the same convention.

Well, that's it for now. As always, if you have any questions or comments
regarding this column, please feel free to contact me at
TS.Kelso@celestrak.com. Until next
time, keep looking up!